Image maximality conjecture for the DH-matrix

Let ${\bf D}$ be the DH-matrix, and say that a matrix is image maximal when it is not properly image dominated by any image partition regular extension. The preceding theorem states that every image partition regular matrix obtained from ${\bf D}$ by adjoining finitely many rows is image dominated by ${\bf D}$.

Image maximality conjecture. The system ${\bf D}$ is image maximal.

The theorem establishes only finite image maximality: every finite-row image partition regular extension is image dominated by ${\bf D}$. The conjecture strengthens this to image maximality without the finite-extension restriction; the supplied text does not state whether it has been resolved.